In what way 'does not work' ? Please state the entire command line, including the input file, the order is important.
Did you get an error ? If so what error ? Did you get anything at all in the back channel ?
Why are you using -dQUIET when trying to debug a problem ? You want all the information Ghostscript can give you about the problem, so drop that.
Please note that Ghostscript does not 'convert' PDF files, and that setting the CompatibilityLevel to 1.5 doesn't really do much. It simply limits the features the pdfwrite device has available to it.
If the input doesn't require higher level features, then the pdfwrite device won't use them. Since your input is a lower version of PDF, it won't use those features and so although the version in the header will be 1.5 the actual content will consist of the lower version features.
You could get the same effect by using a binary-capable editor to change the version in the original PDF file to 1.5.